"I shall now recall to mind that the motion of the heavenly bodies is circular, since the motion appropriate to a sphere is rotation in a circle." (Nicolaus Copernicus, "De revolutionibus orbium coelestium", 1543)
"While every one of the motions of the earth that arise from the actions of the sun, moon, and planets, etc., have been investigated by astronomers, there is one motion which has hitherto escaped the scrutiny of observers - the diurnal rotation round its axis." (William Herschel, "Astronomical Observations on the Rotation of the Planets Round their, Axes made with a View to determine whether the Earth's Diurnal, Motion is perfectly Equable", Philosophical Transactions of the Royal Society of London Vol. 71, 1781)
"The concept of rotation led to geometrical exponential magnitudes, to the analysis of angles and of trigonometric functions, etc. I was delighted how thorough the analysis thus formed and extended, not only the often very complex and unsymmetric formulae which are fundamental in tidal theory, but also the technique of development parallels the concept." (Hermann Grassmann, "Ausdehnungslehre", 1844)
"What distinguishes the straight line and circle more than anything else, and properly separates them for the purpose of elementary geometry? Their self-similarity. Every inch of a straight line coincides with every other inch, and of a circle with every other of the same circle. Where, then, did Euclid fail? In not introducing the third curve, which has the same property - the screw. The right line, the circle, the screw - the representations of translation, rotation, and the two combined - ought to have been the instruments of geometry. With a screw we should never have heard of the impossibility of trisecting an angle, squaring the circle, etc." (Augustus De Morgan, [From Letter to William R Hamilton] 1852)
"What is commonly called the geometrical representation of complex numbers has at least this advantage […] that in it 1 and i do not appear as wholly unconnected and different in kind: the segment taken to represent i stands in a regular relation to the segment which represents 1. […] A complex number, on this interpretation, shows how the segment taken as its representation is reached, starting from a given segment (the unit segment), by means of operations of multiplication, division, and rotation." (Gottlob Frege, "Grundlagen der Arithmetik" ["Foundations of Arithmetic"], 1884)
"When we study the structure of the atom, we shall arrive at the conclusion that it is an immense reservoir of energy solely constituted by a system of imponderable elements maintained in equilibrium by the rotations, attractions and repulsions of its component parts." (Gustave Le Bon, "The Evolution of Matter", 1907)
"The power of differential calculus is that it linearizes all problems by going back to the 'infinitesimally small', but this process can be used only on smooth manifolds. Thus our distinction between the two senses of rotation on a smooth manifold rests on the fact that a continuously differentiable coordinate transformation leaving the origin fixed can be approximated by a linear transformation at О and one separates the (nondegenerate) homogeneous linear transformations into positive and negative according to the sign of their determinants. Also the invariance of the dimension for a smooth manifold follows simply from the fact that a linear substitution which has an inverse preserves the number of variables." (Hermann Weyl, "The Concept of a Riemann Surface", 1913)
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